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<section id="nanowasm">
<h1>NanoWasm<a class="headerlink" href="#nanowasm" title="Link to this heading"></a></h1>
<p><em>NanoWasm</em> is a small language with simple types and instructions.</p>
<section id="abstract-syntax">
<h2>Abstract Syntax<a class="headerlink" href="#abstract-syntax" title="Link to this heading"></a></h2>
<p>The <em>abstract syntax</em> of types is as follows:</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rrl&#64;{}l&#64;{}}
&amp; {\mathit{mut}} &amp; ::= &amp; \mathsf{mut} \\[0.8ex]
&amp; {\mathit{valtype}} &amp; ::= &amp; \mathsf{i{\scriptstyle 32}} ~~|~~ \mathsf{i{\scriptstyle 64}} ~~|~~ \mathsf{f{\scriptstyle 32}} ~~|~~ \mathsf{f{\scriptstyle 64}} \\[0.8ex]
&amp; {\mathit{functype}} &amp; ::= &amp; {{\mathit{valtype}}^\ast} \rightarrow {{\mathit{valtype}}^\ast} \\[0.8ex]
&amp; {\mathit{globaltype}} &amp; ::= &amp; {{\mathit{mut}}^?}~{\mathit{valtype}} \\
\end{array}\end{split}\]</div>
<p>Instructions take the following form:</p>
<div class="math notranslate nohighlight" id="syntax-i32">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rrl&#64;{}l&#64;{}}
&amp; {\mathit{const}} &amp; ::= &amp; 0 ~~|~~ 1 ~~|~~ 2 ~~|~~ \dots \\[0.8ex]
&amp; {\mathit{instr}} &amp; ::= &amp; \mathsf{nop} \\
&amp; &amp; | &amp; \mathsf{drop} \\
&amp; &amp; | &amp; \mathsf{select} \\
&amp; &amp; | &amp; {\mathit{valtype}}{.}\mathsf{const}~{\mathit{const}} \\
&amp; &amp; | &amp; \mathsf{local{.}get}~{\mathit{localidx}} \\
&amp; &amp; | &amp; \mathsf{local{.}set}~{\mathit{localidx}} \\
&amp; &amp; | &amp; \mathsf{global{.}get}~{\mathit{globalidx}} \\
&amp; &amp; | &amp; \mathsf{global{.}set}~{\mathit{globalidx}} \\
\end{array}\end{split}\]</div>
<p>The instruction <span class="math notranslate nohighlight">\(\mathsf{nop}\)</span> does nothing,
<span class="math notranslate nohighlight">\(\mathsf{drop}\)</span> removes an operand from the stack,
<span class="math notranslate nohighlight">\(\mathsf{select}\)</span> picks one of two operands depending on a condition value.
The instruction <span class="math notranslate nohighlight">\(t{.}\mathsf{const}~c\)</span> pushed the constant <span class="math notranslate nohighlight">\(c\)</span> to the stack.
The remaining instructions access local and global variables.</p>
</section>
<section id="validation">
<h2>Validation<a class="headerlink" href="#validation" title="Link to this heading"></a></h2>
<p>NanoWasm instructions are <em>type-checked</em> under a context that assigns types to indices:</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rrl&#64;{}l&#64;{}}
&amp; {\mathit{context}} &amp; ::= &amp; \{ \begin{array}[t]{&#64;{}l&#64;{}l&#64;{}}
\mathsf{globals}~{{\mathit{globaltype}}^\ast} , \mathsf{locals}~{{\mathit{valtype}}^\ast} \} \\
\end{array} \\
\end{array}\end{split}\]</div>
<section id="mathsf-nop">
<h3><span class="math notranslate nohighlight">\(\mathsf{nop}\)</span><a class="headerlink" href="#mathsf-nop" title="Link to this heading"></a></h3>
<p><span class="math notranslate nohighlight">\(\mathsf{nop}\)</span> is <a class="reference internal" href="#valid-val"><span class="std std-ref">valid</span></a> with <span class="math notranslate nohighlight">\(\epsilon~\rightarrow~\epsilon\)</span>.</p>
<div class="math notranslate nohighlight">
\[\begin{array}{&#64;{}c&#64;{}}\displaystyle
\frac{
}{
C \vdash \mathsf{nop} : \epsilon \rightarrow \epsilon
}
\qquad
\end{array}\]</div>
</section>
<section id="mathsf-drop">
<h3><span class="math notranslate nohighlight">\(\mathsf{drop}\)</span><a class="headerlink" href="#mathsf-drop" title="Link to this heading"></a></h3>
<p><span class="math notranslate nohighlight">\(\mathsf{drop}\)</span> is <a class="reference internal" href="#valid-val"><span class="std std-ref">valid</span></a> with <span class="math notranslate nohighlight">\(t~\rightarrow~\epsilon\)</span>.</p>
<div class="math notranslate nohighlight">
\[\begin{array}{&#64;{}c&#64;{}}\displaystyle
\frac{
}{
C \vdash \mathsf{drop} : t \rightarrow \epsilon
}
\qquad
\end{array}\]</div>
</section>
<section id="mathsf-select">
<h3><span class="math notranslate nohighlight">\(\mathsf{select}\)</span><a class="headerlink" href="#mathsf-select" title="Link to this heading"></a></h3>
<p><span class="math notranslate nohighlight">\(\mathsf{select}\)</span> is <a class="reference internal" href="#valid-val"><span class="std std-ref">valid</span></a> with <span class="math notranslate nohighlight">\(t~t~\mathsf{i{\scriptstyle 32}}~\rightarrow~t\)</span>.</p>
<div class="math notranslate nohighlight">
\[\begin{array}{&#64;{}c&#64;{}}\displaystyle
\frac{
}{
C \vdash \mathsf{select} : t~t~\mathsf{i{\scriptstyle 32}} \rightarrow t
}
\qquad
\end{array}\]</div>
</section>
<section id="mathsf-const">
<span id="valid-val"></span><h3><span class="math notranslate nohighlight">\(\mathsf{const}\)</span><a class="headerlink" href="#mathsf-const" title="Link to this heading"></a></h3>
<p><span class="math notranslate nohighlight">\((t{.}\mathsf{const}~c)\)</span> is <a class="reference internal" href="#valid-val"><span class="std std-ref">valid</span></a> with <span class="math notranslate nohighlight">\(\epsilon~\rightarrow~t\)</span>.</p>
<div class="math notranslate nohighlight">
\[\begin{array}{&#64;{}c&#64;{}}\displaystyle
\frac{
}{
C \vdash t{.}\mathsf{const}~c : \epsilon \rightarrow t
}
\qquad
\end{array}\]</div>
</section>
<section id="mathsf-local-get">
<h3><span class="math notranslate nohighlight">\(\mathsf{local{.}get}\)</span><a class="headerlink" href="#mathsf-local-get" title="Link to this heading"></a></h3>
<p><span class="math notranslate nohighlight">\((\mathsf{local{.}get}~x)\)</span> is <a class="reference internal" href="#valid-val"><span class="std std-ref">valid</span></a> with <span class="math notranslate nohighlight">\(\epsilon~\rightarrow~t\)</span> if:</p>
<blockquote>
<div><ul class="simple">
<li><p><span class="math notranslate nohighlight">\(C{.}\mathsf{locals}{}[x]\)</span> exists.</p></li>
<li><p><span class="math notranslate nohighlight">\(C{.}\mathsf{locals}{}[x]\)</span> is of the form <span class="math notranslate nohighlight">\(t\)</span>.</p></li>
</ul>
</div></blockquote>
<div class="math notranslate nohighlight">
\[\begin{array}{&#64;{}c&#64;{}}\displaystyle
\frac{
C{.}\mathsf{locals}{}[x] = t
}{
C \vdash \mathsf{local{.}get}~x : \epsilon \rightarrow t
}
\qquad
\end{array}\]</div>
</section>
<section id="mathsf-local-set">
<h3><span class="math notranslate nohighlight">\(\mathsf{local{.}set}\)</span><a class="headerlink" href="#mathsf-local-set" title="Link to this heading"></a></h3>
<p><span class="math notranslate nohighlight">\((\mathsf{local{.}set}~x)\)</span> is <a class="reference internal" href="#valid-val"><span class="std std-ref">valid</span></a> with <span class="math notranslate nohighlight">\(t~\rightarrow~\epsilon\)</span> if:</p>
<blockquote>
<div><ul class="simple">
<li><p><span class="math notranslate nohighlight">\(C{.}\mathsf{locals}{}[x]\)</span> exists.</p></li>
<li><p><span class="math notranslate nohighlight">\(C{.}\mathsf{locals}{}[x]\)</span> is of the form <span class="math notranslate nohighlight">\(t\)</span>.</p></li>
</ul>
</div></blockquote>
<div class="math notranslate nohighlight">
\[\begin{array}{&#64;{}c&#64;{}}\displaystyle
\frac{
C{.}\mathsf{locals}{}[x] = t
}{
C \vdash \mathsf{local{.}set}~x : t \rightarrow \epsilon
}
\qquad
\end{array}\]</div>
</section>
<section id="mathsf-global-get">
<h3><span class="math notranslate nohighlight">\(\mathsf{global{.}get}\)</span><a class="headerlink" href="#mathsf-global-get" title="Link to this heading"></a></h3>
<p><span class="math notranslate nohighlight">\((\mathsf{global{.}get}~x)\)</span> is <a class="reference internal" href="#valid-val"><span class="std std-ref">valid</span></a> with <span class="math notranslate nohighlight">\(\epsilon~\rightarrow~t\)</span> if:</p>
<blockquote>
<div><ul class="simple">
<li><p><span class="math notranslate nohighlight">\(C{.}\mathsf{globals}{}[x]\)</span> exists.</p></li>
<li><p><span class="math notranslate nohighlight">\(C{.}\mathsf{globals}{}[x]\)</span> is of the form <span class="math notranslate nohighlight">\(({\mathsf{mut}^?}~t)\)</span>.</p></li>
</ul>
</div></blockquote>
<div class="math notranslate nohighlight">
\[\begin{array}{&#64;{}c&#64;{}}\displaystyle
\frac{
C{.}\mathsf{globals}{}[x] = {\mathsf{mut}^?}~t
}{
C \vdash \mathsf{global{.}get}~x : \epsilon \rightarrow t
}
\qquad
\end{array}\]</div>
</section>
<section id="mathsf-global-set">
<h3><span class="math notranslate nohighlight">\(\mathsf{global{.}set}\)</span><a class="headerlink" href="#mathsf-global-set" title="Link to this heading"></a></h3>
<p><span class="math notranslate nohighlight">\((\mathsf{global{.}get}~x)\)</span> is <a class="reference internal" href="#valid-val"><span class="std std-ref">valid</span></a> with <span class="math notranslate nohighlight">\(t~\rightarrow~\epsilon\)</span> if:</p>
<blockquote>
<div><ul class="simple">
<li><p><span class="math notranslate nohighlight">\(C{.}\mathsf{globals}{}[x]\)</span> exists.</p></li>
<li><p><span class="math notranslate nohighlight">\(C{.}\mathsf{globals}{}[x]\)</span> is of the form <span class="math notranslate nohighlight">\((\mathsf{mut}~t)\)</span>.</p></li>
</ul>
</div></blockquote>
<div class="math notranslate nohighlight">
\[\begin{array}{&#64;{}c&#64;{}}\displaystyle
\frac{
C{.}\mathsf{globals}{}[x] = \mathsf{mut}~t
}{
C \vdash \mathsf{global{.}get}~x : t \rightarrow \epsilon
}
\qquad
\end{array}\]</div>
</section>
</section>
<section id="execution">
<h2>Execution<a class="headerlink" href="#execution" title="Link to this heading"></a></h2>
<p>NanoWasm execution requires a suitable definition of state and configuration:</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rrl&#64;{}l&#64;{}}
&amp; {\mathit{addr}} &amp; ::= &amp; 0 ~~|~~ 1 ~~|~~ 2 ~~|~~ \dots \\
&amp; {\mathit{moduleinst}} &amp; ::= &amp; \{ \begin{array}[t]{&#64;{}l&#64;{}l&#64;{}}
\mathsf{globals}~{{\mathit{addr}}^\ast} \} \\
\end{array} \\[0.8ex]
&amp; {\mathit{val}} &amp; ::= &amp; \mathsf{const}~{\mathit{valtype}}~{\mathit{const}} \\[0.8ex]
&amp; {\mathit{store}} &amp; ::= &amp; \{ \begin{array}[t]{&#64;{}l&#64;{}l&#64;{}}
\mathsf{globals}~{{\mathit{val}}^\ast} \} \\
\end{array} \\
&amp; {\mathit{frame}} &amp; ::= &amp; \{ \begin{array}[t]{&#64;{}l&#64;{}l&#64;{}}
\mathsf{locals}~{{\mathit{val}}^\ast} , \mathsf{module}~{\mathit{moduleinst}} \} \\
\end{array} \\
&amp; {\mathit{state}} &amp; ::= &amp; {\mathit{store}} ; {\mathit{frame}} \\
&amp; {\mathit{config}} &amp; ::= &amp; {\mathit{state}} ; {{\mathit{instr}}^\ast} \\
\end{array}\end{split}\]</div>
<p>We define the following auxiliary functions for accessing and updating the state:</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}lcl&#64;{}l&#64;{}}
{\mathrm{local}}((s ; f), x) &amp; = &amp; f{.}\mathsf{locals}{}[x] \\
{\mathrm{global}}((s ; f), x) &amp; = &amp; s{.}\mathsf{globals}{}[f{.}\mathsf{module}{.}\mathsf{globals}{}[x]] \\[0.8ex]
{\mathrm{update}}_{\mathit{local}}((s ; f), x, v) &amp; = &amp; s ; f{}[{.}\mathsf{locals}{}[x] = v] \\
{\mathrm{update}}_{\mathit{global}}((s ; f), x, v) &amp; = &amp; s{}[{.}\mathsf{globals}{}[f{.}\mathsf{module}{.}\mathsf{globals}{}[x]] = v] ; f \\
\end{array}\end{split}\]</div>
<p>With that, execution is defined as follows:</p>
<section id="id1">
<h3><span class="math notranslate nohighlight">\(\mathsf{nop}\)</span><a class="headerlink" href="#id1" title="Link to this heading"></a></h3>
<ol class="arabic simple">
<li><p>Do nothing.</p></li>
</ol>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rcl&#64;{}l&#64;{}}
&amp; \mathsf{nop} &amp; \hookrightarrow &amp; \epsilon \\
\end{array}\end{split}\]</div>
</section>
<section id="id2">
<h3><span class="math notranslate nohighlight">\(\mathsf{drop}\)</span><a class="headerlink" href="#id2" title="Link to this heading"></a></h3>
<ol class="arabic simple">
<li><p>Assert: Due to validation, a value is on the top of the stack.</p></li>
<li><p>Pop the value <span class="math notranslate nohighlight">\({\mathit{val}}\)</span> from the stack.</p></li>
</ol>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rcl&#64;{}l&#64;{}}
&amp; {\mathit{val}}~\mathsf{drop} &amp; \hookrightarrow &amp; \epsilon \\
\end{array}\end{split}\]</div>
</section>
<section id="id3">
<h3><span class="math notranslate nohighlight">\(\mathsf{select}\)</span><a class="headerlink" href="#id3" title="Link to this heading"></a></h3>
<ol class="arabic simple">
<li><p>Assert: Due to validation, a value of valtype <span class="math notranslate nohighlight">\(\mathsf{i{\scriptstyle 32}}\)</span> is on the top of the stack.</p></li>
<li><p>Pop the value <span class="math notranslate nohighlight">\((\mathsf{i{\scriptstyle 32}}{.}\mathsf{const}~c)\)</span> from the stack.</p></li>
<li><p>Assert: Due to validation, a value is on the top of the stack.</p></li>
<li><p>Pop the value <span class="math notranslate nohighlight">\({\mathit{val}}_2\)</span> from the stack.</p></li>
<li><p>Assert: Due to validation, a value is on the top of the stack.</p></li>
<li><p>Pop the value <span class="math notranslate nohighlight">\({\mathit{val}}_1\)</span> from the stack.</p></li>
<li><p>If <span class="math notranslate nohighlight">\(c \neq 0\)</span>, then:</p>
<ol class="loweralpha simple">
<li><p>Push the value <span class="math notranslate nohighlight">\({\mathit{val}}_1\)</span> to the stack.</p></li>
</ol>
</li>
<li><p>Else:</p>
<ol class="loweralpha simple">
<li><p>Push the value <span class="math notranslate nohighlight">\({\mathit{val}}_2\)</span> to the stack.</p></li>
</ol>
</li>
</ol>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rcl&#64;{}l&#64;{}}
&amp; {\mathit{val}}_1~{\mathit{val}}_2~(\mathsf{i{\scriptstyle 32}}{.}\mathsf{const}~c)~\mathsf{select} &amp; \hookrightarrow &amp; {\mathit{val}}_1 &amp; \quad \mbox{if}~ c \neq 0 \\[0.8ex]
&amp; {\mathit{val}}_1~{\mathit{val}}_2~(\mathsf{i{\scriptstyle 32}}{.}\mathsf{const}~c)~\mathsf{select} &amp; \hookrightarrow &amp; {\mathit{val}}_2 &amp; \quad \mbox{otherwise} \\
\end{array}\end{split}\]</div>
</section>
<section id="mathsf-local-get-x">
<h3><span class="math notranslate nohighlight">\(\mathsf{local{.}get}~x\)</span><a class="headerlink" href="#mathsf-local-get-x" title="Link to this heading"></a></h3>
<ol class="arabic simple">
<li><p>Let <span class="math notranslate nohighlight">\(z\)</span> be the current state.</p></li>
<li><p>Let <span class="math notranslate nohighlight">\({\mathit{val}}\)</span> be <span class="math notranslate nohighlight">\({\mathrm{local}}(z, x)\)</span>.</p></li>
<li><p>Push the value <span class="math notranslate nohighlight">\({\mathit{val}}\)</span> to the stack.</p></li>
</ol>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rcl&#64;{}l&#64;{}}
&amp; z ; (\mathsf{local{.}get}~x) &amp; \hookrightarrow &amp; z ; {\mathit{val}} &amp; \quad \mbox{if}~ {\mathit{val}} = {\mathrm{local}}(z, x) \\
\end{array}\end{split}\]</div>
</section>
<section id="mathsf-local-set-x">
<h3><span class="math notranslate nohighlight">\(\mathsf{local{.}set}~x\)</span><a class="headerlink" href="#mathsf-local-set-x" title="Link to this heading"></a></h3>
<ol class="arabic simple">
<li><p>Assert: Due to validation, a value is on the top of the stack.</p></li>
<li><p>Pop the value <span class="math notranslate nohighlight">\({\mathit{val}}\)</span> from the stack.</p></li>
</ol>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rcl&#64;{}l&#64;{}}
&amp; z ; {\mathit{val}}~(\mathsf{local{.}set}~x) &amp; \hookrightarrow &amp; {z'} ; \epsilon &amp; \quad \mbox{if}~ {z'} = {\mathrm{update}}_{\mathit{local}}(z, x, {\mathit{val}}) \\
\end{array}\end{split}\]</div>
</section>
<section id="mathsf-global-get-x">
<h3><span class="math notranslate nohighlight">\(\mathsf{global{.}get}~x\)</span><a class="headerlink" href="#mathsf-global-get-x" title="Link to this heading"></a></h3>
<ol class="arabic simple">
<li><p>Let <span class="math notranslate nohighlight">\(z\)</span> be the current state.</p></li>
<li><p>Let <span class="math notranslate nohighlight">\({\mathit{val}}\)</span> be <span class="math notranslate nohighlight">\({\mathrm{global}}(z, x)\)</span>.</p></li>
<li><p>Push the value <span class="math notranslate nohighlight">\({\mathit{val}}\)</span> to the stack.</p></li>
</ol>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rcl&#64;{}l&#64;{}}
&amp; z ; (\mathsf{global{.}get}~x) &amp; \hookrightarrow &amp; z ; {\mathit{val}} &amp; \quad \mbox{if}~ {\mathit{val}} = {\mathrm{global}}(z, x) \\
\end{array}\end{split}\]</div>
</section>
<section id="mathsf-global-set-x">
<h3><span class="math notranslate nohighlight">\(\mathsf{global{.}set}~x\)</span><a class="headerlink" href="#mathsf-global-set-x" title="Link to this heading"></a></h3>
<ol class="arabic simple">
<li><p>Assert: Due to validation, a value is on the top of the stack.</p></li>
<li><p>Pop the value <span class="math notranslate nohighlight">\({\mathit{val}}\)</span> from the stack.</p></li>
</ol>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rcl&#64;{}l&#64;{}}
&amp; z ; {\mathit{val}}~(\mathsf{global{.}set}~x) &amp; \hookrightarrow &amp; {z'} ; \epsilon &amp; \quad \mbox{if}~ {z'} = {\mathrm{update}}_{\mathit{global}}(z, x, {\mathit{val}}) \\
\end{array}\end{split}\]</div>
</section>
</section>
<section id="binary-format">
<h2>Binary Format<a class="headerlink" href="#binary-format" title="Link to this heading"></a></h2>
<p>The following grammars define the binary representation of NanoWasm programs.</p>
<p>First, constants are represented in LEB format:</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rrl&#64;{}l&#64;{}l&#64;{}l&#64;{}}
&amp; {\mathtt{byte}} &amp; ::= &amp; \mathtt{0x00} ~~|~~ \ldots ~~|~~ \mathtt{0xFF} \\[0.8ex]
&amp; {\mathtt{u}}(N) &amp; ::= &amp; n{:}{\mathtt{byte}} &amp; \quad\Rightarrow\quad{} &amp; n &amp; \quad \mbox{if}~ n &lt; {2^{7}} \land n &lt; {2^{N}} \\
&amp; &amp; | &amp; n{:}{\mathtt{byte}}~~m{:}{\mathtt{u}}(N - 7) &amp; \quad\Rightarrow\quad{} &amp; {2^{7}} \cdot m + (n - {2^{7}}) &amp; \quad \mbox{if}~ n \geq {2^{7}} \land N &gt; 7 \\[0.8ex]
&amp; {\mathtt{u32}} &amp; ::= &amp; {\mathtt{u}}(32) \\
&amp; {\mathtt{u64}} &amp; ::= &amp; {\mathtt{u}}(64) \\[0.8ex]
&amp; {\mathtt{f}}(N) &amp; ::= &amp; {b^\ast}{:}{{\mathtt{byte}}^{N / 8}} &amp; \quad\Rightarrow\quad{} &amp; {\mathrm{float}}(N, {b^\ast}) \\[0.8ex]
&amp; {\mathtt{f32}} &amp; ::= &amp; {\mathtt{f}}(32) \\
&amp; {\mathtt{f64}} &amp; ::= &amp; {\mathtt{f}}(64) \\
\end{array}\end{split}\]</div>
<p>Types are encoded as follows:</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rrl&#64;{}l&#64;{}l&#64;{}l&#64;{}}
&amp; {\mathtt{valtype}} &amp; ::= &amp; \mathtt{0x7F} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{i{\scriptstyle 32}} \\
&amp; &amp; | &amp; \mathtt{0x7E} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{i{\scriptstyle 64}} \\
&amp; &amp; | &amp; \mathtt{0x7D} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{f{\scriptstyle 32}} \\
&amp; &amp; | &amp; \mathtt{0x7C} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{f{\scriptstyle 64}} \\[0.8ex]
&amp; {\mathtt{mut}} &amp; ::= &amp; \mathtt{0x00} &amp; \quad\Rightarrow\quad{} &amp; \epsilon \\
&amp; &amp; | &amp; \mathtt{0x01} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{mut} \\[0.8ex]
&amp; {\mathtt{globaltype}} &amp; ::= &amp; t{:}{\mathtt{valtype}}~~{\mathit{mut}}{:}{\mathtt{mut}} &amp; \quad\Rightarrow\quad{} &amp; {\mathit{mut}}~t \\
&amp; {\mathtt{resulttype}} &amp; ::= &amp; n{:}{\mathtt{u32}}~~{(t{:}{\mathtt{valtype}})^{n}} &amp; \quad\Rightarrow\quad{} &amp; {t^{n}} \\
&amp; {\mathtt{functype}} &amp; ::= &amp; \mathtt{0x60}~~{t_1^\ast}{:}{\mathtt{resulttype}}~~{t_2^\ast}{:}{\mathtt{resulttype}} &amp; \quad\Rightarrow\quad{} &amp; {t_1^\ast} \rightarrow {t_2^\ast} \\
\end{array}\end{split}\]</div>
<p>Finally, instruction opcodes:</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{array}[t]{&#64;{}l&#64;{}rrl&#64;{}l&#64;{}l&#64;{}l&#64;{}}
&amp; {\mathtt{globalidx}} &amp; ::= &amp; x{:}{\mathtt{u32}} &amp; \quad\Rightarrow\quad{} &amp; x \\
&amp; {\mathtt{localidx}} &amp; ::= &amp; x{:}{\mathtt{u32}} &amp; \quad\Rightarrow\quad{} &amp; x \\[0.8ex]
&amp; {\mathtt{instr}} &amp; ::= &amp; \mathtt{0x01} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{nop} \\
&amp; &amp; | &amp; \mathtt{0x1A} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{drop} \\
&amp; &amp; | &amp; \mathtt{0x1B} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{select} \\
&amp; &amp; | &amp; \mathtt{0x20}~~x{:}{\mathtt{localidx}} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{local{.}get}~x \\
&amp; &amp; | &amp; \mathtt{0x21}~~x{:}{\mathtt{localidx}} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{local{.}set}~x \\
&amp; &amp; | &amp; \mathtt{0x23}~~x{:}{\mathtt{globalidx}} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{global{.}get}~x \\
&amp; &amp; | &amp; \mathtt{0x24}~~x{:}{\mathtt{globalidx}} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{global{.}set}~x \\
&amp; &amp; | &amp; \mathtt{0x41}~~n{:}{\mathtt{u32}} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{i{\scriptstyle 32}}{.}\mathsf{const}~n \\
&amp; &amp; | &amp; \mathtt{0x42}~~n{:}{\mathtt{u64}} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{i{\scriptstyle 64}}{.}\mathsf{const}~n \\
&amp; &amp; | &amp; \mathtt{0x43}~~p{:}{\mathtt{f32}} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{f{\scriptstyle 32}}{.}\mathsf{const}~p \\
&amp; &amp; | &amp; \mathtt{0x44}~~p{:}{\mathtt{f64}} &amp; \quad\Rightarrow\quad{} &amp; \mathsf{f{\scriptstyle 64}}{.}\mathsf{const}~p \\
\end{array}\end{split}\]</div>
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